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Recently, Curto, Lee and Yoon considered the properties (such as, hyponormality, subnormality, and flatness, etc.) for $2$-variable weighted shifts and constructed several families of commuting pairs of subnormal operators such that each family can be used to answer a conjecture of Curto, Muhly and Xia negatively. In this paper, we consider the weak and quadratic hyponormality of 2-variable weighted shifts $\left( W_{1},W_{2}\right) $. In addition, we detect the weak and quadratic hyponormality with some interesting 2-variable weighted shifts.
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참고문헌 (13)
참고문헌 신청
C. Li / 2003 / Two variable subnormal completion problem / Hokkaido Math. J 32 (1) : 21 ~ 29
C. Li / 2009 / The characteristics of expansivity of two variable weighted shift / Integral Equations Operator Theory 65 (3) : 405 ~ 414
G. Exner / 2006 / Weakly n-hyponormal weighted shifts and their examples / Integral Equations Opertor Theory 54 (2) : 215 ~ 233
J. Kim / 2015 / Flat phenomena of 2-variable weighted shifts / Linear Algebra Appl 486 : 234 ~ 254
J. Kim / 2016 / Hyponormality for commuting pairs of operators / J. Math. Anal. Appl 434 (2) : 1077 ~ 1090
C. Li / 2009 / The characteristics of expansivity of two variable weighted shift / Integral Equations Operator Theory 65 (3) : 405 ~ 414
G. Exner / 2006 / Weakly n-hyponormal weighted shifts and their examples / Integral Equations Opertor Theory 54 (2) : 215 ~ 233
J. Kim / 2015 / Flat phenomena of 2-variable weighted shifts / Linear Algebra Appl 486 : 234 ~ 254
J. Kim / 2016 / Hyponormality for commuting pairs of operators / J. Math. Anal. Appl 434 (2) : 1077 ~ 1090
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